July 27, 1905] 



NA TURE 



29: 



ethics, are well brought out by this author. His 

 book may be heartily recommended to students of 

 the period described. 



1 Text-book of Phvsics, Heat. By Prof. J. H. 

 Poynting, Sc.D., F.R.S., and Prof. J. J. Thomson, 

 M.'A., F.R.S. Pp. xvi + 354. (London: C. Griffin 

 and Co., Ltd., 1904.) Price 15s. 

 The third volume of this well known text-book more 

 than sustains the standard set by its predecessors. 

 The volumes on sound and properties of matter have 

 already appeared. The volumes on light and on 

 electricity and magnetism we hope may follow at a 

 somewhat shorter interval than has intervened 

 between the first three volumes of the series. It is 

 hardly necessary to say that the work is well up to 

 date, 'and extremely clear and exact throughout, and 

 that it is as complete as it would be possible to make 

 such a text-book within the limits which the authois 

 have laid down for the scope of their work. Among 

 the more original features which should be valuable 

 to the student as filling gaps which are noticeable in 

 similar text-books, we observe that a useful chapter 

 is included on the subject of circulation and convec- 

 tion, with illustrations from meteorology and ventil- 

 ation. The treatment of the important subject of 

 radiation, especially in relation to temperature and 

 thermodynamics, is unusually complete and clear, and 

 presents in a simple, connected form a number of 

 most important results which the student would have 

 difficulty in finding elsewhere. The experimental 

 spirit is maintained throughout the work in such a 

 manner that the student will feel that he is learning 

 from a practical master of the subject, and will un- 

 consciously imbibe something of the attitude of mind 

 of the original investigator. H. L. C. 



The Oxford Atlas of the British Colonies. Part i. 

 British Africa. Seventeen maps. (Oxford Geo- 

 graphical Institute : William Stanford and Co., 

 Ltd., n.d.) Price 2.S. bd. net. 

 The first thirteen plates consist of coloured maps, and 

 the remaining four are outlines intended for use as 

 " test " maps or for other class purposes. The first 

 map shows a hemisphere in which Cape Colony 

 occupies the centre, and it is possible from it to see 

 at once the relation of South .\frica to the other 

 continents. Map ii. is a political map of the world 

 drawn in accordance with Mollweides's equal area 

 projection, and the student will notice at a glance the 

 apparent distortion in shape, though the relative 

 sizes of land areas in different parts of the map are 

 correctlv shown. In addition to meteorological charts, 

 the atlas includes physical and political maps of 

 Africa, and maps of Cape Colony, Natal and Zulu- 

 limd, the Transvaal and Orange River Colony, 

 Rhodesia, and of West, East, and Central Africa. 



Wii,'/i Temperature Measurements. Bv H. Le Chate- 

 lier and O. Boudouard. Authorised translation and 

 additions by Dr. G. K. Burgess. Second edition. 

 Pp. XV + 341. (New York: Jolin Wiley and Sons; 

 London : Chapman and Hall, Ltd., 1904.) Price 

 12s. bd. net. 

 In preparing the present edition it was found neces- 

 sary to make a large number of additions, and the 

 book now gives a useful summary of what is known 

 .ibout pyromctry. The advances in optical pyrometry 

 during the last few years are recognised by the 

 .luthors, and a useful chapter on the laws of radiation 

 has been inserted. A number of pyrometers are de- 

 scribed, but the discussion of the principles involved 

 is in general more adequate than the description of 

 instruments. No mention is made of some of the 

 best of these in use in this countrv. 



NO. 1865, VOL. 72] 



LETTERS TO THE EDITOR. 



[The Editor does )iot hold himself responsible for opinions 

 •expressed fay his correspondents. Neither can he undertake 

 to return, or to correspond with the writers of, rejected 

 numuscripts intended for this or any other part of Nature. 

 Ao notice is taken of anonymous communications.] 



A Comparison between Two Theories of Radiation. 



On two occasions (Nature, May 18 and July 13) Lord; 

 Rayleigh has asked for a critical comparison of two 

 theories of radiation, the one developed by Prof. Planck 

 {Drude's Annalen, i. p. 69, and iv. p. 553) and the other 

 bv myself, following the dynamical principles laid down 

 by Maxwell and Lord Rayleigh. It is with the greatest 

 hesitation that I venture to express my disagreement with 

 some points in the work of so distinguished a physicist as 

 Prof. Planck, but Lord Rayleigh 's second demand for a 

 comparison of the two methods leads me to offer the follow- 

 ing remarks, which would not otherwise have been pub- 

 lished, on the theory of Prof. Planck. 



Early in his second paper, Planck introduces the con- 

 ception of the " entropy of a single resonator " S. There 

 are supposed to be N resonators having a total entropy 

 S^- = \S, and Ss is supposed to be given by Ss = -(■ 

 log W + constant, where W is the " probability " that the N 

 resonators shall be as they are. Without discussing the 

 legitimacy of assigning entropy to a single resonator, we 

 may at present suppose S defined by S = fe/N log W + cons. 



The function W, as at present defined, seems to me to 

 have no meaning. Planck (in common, I know, with 

 many other physicists) speaks of the " probability " of an 

 event, without specifying the basis according to which the 

 probability is measured. This conception of probability 

 seems to me an inexact conception, and as such to have no 

 place in mathematical analysis. For instance, a mathe- 

 matician has no right, qtid mathematician, to speak of 

 the probability that a tree shall be between six and seven 

 feet in height unless he at the same time specifies from 

 what trees the tree in question is to be selected, and how. 

 If this is not so, may I ask, " .What is the probability 

 that a tree shall be between six and seven feet high? " 



When Prof. Planck calculates the probability function 

 W, he in effect assumes that a priori equal small ranges 

 of energy are equally probable. Thus he tacitly introduces 

 as the basis of his probability calculations an ensemble 

 of systems of resonators such that the number^ of systems 

 in which the energy of any given resonator lies between 

 E and E + dE is proportional simply to dE. This, of 

 course, he has a right to do, only he must continue to 

 measure probability according to this same basis. 



The systems of resonators are in motion, their motion 

 being governed by the laws of dynamics. Will they, as 

 the motion progresses, retain the statistical property which 

 has been the cause of their introduction, namely, that the 

 number of systems in which the energy of any given 

 resonator lies between E and E + dE is proportional simply 

 to dE? It is easily found, by the method explained in my 

 " Dvnamical Theory of Gases" (§ 211), that in general 

 they will not ; the probability function W is not simply a 

 function of the coordinates of the system. Prof. Planck's 

 position is as though he had attempted to calculate the 

 probability that a tree should be between six and seven 

 feet high,' taking as his basis of calculation an enclosure 

 of growing trees, and assuming the probability to be a 

 function only of the quantities six and seven feet. His 

 ensemble of systems has not yet reached a statistical 

 " steady state." 



Prof. Planck supposes his function S to possess the 

 property of the entropy function, so that i/T = (iS/dU, 

 where ' T is the temperature. Combining this with 

 Planck's calculation of S, we find 



l/T = ^-/^log(i+./U) .... (I) 

 Here e is a small quantity, a sort of indivisible atom 

 of energy, introduced to simplify the calculations. We 

 may legitimately remove this artificial quantity by passing 

 to the limit in which 6 = 0. In this way we obtain 



i/T = /tVU (2) 



Thus the mean energy of each resonator, according to 

 this equation, is the same multiple of the temperature, no 



